Meta-Analysis in Stata, 2nd edition p.158 Exercise Silgay et al. (2004)
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1 Stata LightStone Stata 14 Funnel StataPress Meta-Analysis in Stata, 2nd edition p.153 Harbord et al. metabias metabias Steichen (1998) Begg Egger Stata Stata metabias Begg Egger Harbord Peters ado metafunnel metan metabias. which metafunnel c:\ado\plus\m\metafunnel.ado *! 1.4.0, Jonathan Sterne & Roger Harbord, 21 May 2004 (SJ4-2: st0061). which metan c:\ado\plus\m\metan.ado *! Sep2010. which metabias c:\ado\plus\m\metabias.ado *! version January 2009 *! Modified regression test for funnel plot asymmetry in 2x2 tables *! based on statistics of score test instead of Wald test. *! Author: roger.harbord@bristol.ac.uk *! Peters test (effect size on 1/N) added *! updates added by Ross Harris *! version sep97 TJS Harbord et al. (2009) nicotinegum.dta Meta-Analysis in Stata, 2nd edition p.158 Exercise Silgay et al. (2004). use nicotinegum, clear (Nicotine gum for smoking cessation) 1
2 . des Contains data from nicotinegum.dta obs: 51 Nicotine gum for smoking cessation vars: 5 8 Jan :02 size: 459 (_dta has notes) storage display value variable name type format label variable label trialid byte %9.0g d1 int %8.0g Intervention successes h1 int %9.0g Intervention failures d0 int %8.0g Control successes h0 int %9.0g Control failures Sorted by: trialid ( 157 ) d (disease) h (healthy) 1( ) d 1 h 1 n 1 2( ) d 0 h 0 n 0 d h n log (OR) OR = (d 1 /h 1 ) / (d 0 /h 0 ) = d 1h 0 d 0 h 1 SE (log (OR)) = 1 d h d h 0 (1). metan d1 h1 d0 h0, or nograph Study OR [95% Conf. Interval] % Weight
3 M-H pooled OR Heterogeneity chi-squared = (d.f. = 50) p = I-squared (variation in OR attributable to heterogeneity) = 19.4% Test of OR=1 : z= p = M-H % 1 I % 25% 1 metan Stata Stata ES logor seloges 3
4 1.5 1 s.e. of logor.5 0. gen logor=log( _ES). gen selogor= _seloges metafunnel Funnel egger. metafunnel logor selogor, egger Funnel plot w ith pseudo 95% confidence limits logor 1: Egger small-study effects( ) 1 Egger metabias metabias Egger Begg Stata metabias Stata 4
5 Journal The Stata Technical Bulletin Steichen (1998) 1 metabias 2 Egger Harbord Peters 4 Begg Begg and Mazumdar (1994) metabias d1 h1 d0 h0, begg Note: data input format tcases tnoncases ccases cnoncases assumed. Note: odds ratios assumed as effect estimate of interest Note: Peters or Harbord tests generally recommended for binary data Begg s test for small-study effects: Rank correlation between standardized intervention effect and its standard error adj. Kendall s Score (P-Q) = 149 Std. Dev. of Score = Number of Studies = 51 z = 1.21 Pr > z = z = 1.20 (continuity corrected) Pr > z = (continuity corrected) z ( ) Egger. metabias d1 h1 d0 h0, egger Note: data input format tcases tnoncases ccases cnoncases assumed. Note: odds ratios assumed as effect estimate of interest Note: Peters or Harbord tests generally recommended for binary data Egger s test for small-study effects: Regress standard normal deviate of intervention effect estimate against its standard error 1 Meta-Analysis in Stata, 2nd edition p166 5
6 Number of studies = 51 Root MSE = Std_Eff Coef. Std. Err. t P> t [95% Conf. Interval] slope bias Test of H0: no small-study effects P = bias p % logor selogor Egger. metabias logor selogor, egger ( ) Stata Harbord Egger Harbord Meta-Analysis in Stata, 2nd edition p.157. metabias d1 h1 d0 h0, harbord graph Note: data input format tcases tnoncases ccases cnoncases assumed. Note: odds ratios assumed as effect estimate of interest Harbord s modified test for small-study effects: Regress Z/sqrt(V) on sqrt(v) where Z is efficient score and V is score variance Number of studies = 51 Root MSE = Z/sqrt(V) Coef. Std. Err. t P> t [95% Conf. Interval] sqrt(v) bias Test of H0: no small-study effects P = p Egger p Harbord 6
7 2 0 2 Z / sqrt(v) sqrt(v) Study regression line 95% CI for intercept 2: Galbraith graph Galbraith Harbord bias 95% 0 0 metafunnel egger Peters. metabias d1 h1 d0 h0, peters Note: data input format tcases tnoncases ccases cnoncases assumed. Note: odds ratios assumed as effect estimate of interest Peter s test for small-study effects: Regress intervention effect estimate on 1/Ntot, with weights SF/Ntot Number of studies = 51 Root MSE =.3897 Std_Eff Coef. Std. Err. t P> t [95% Conf. Interval] bias constant Test of H0: no small-study effects P = bias p Harbord Egger 7
8 Begg Egger Meta-Analysis in Stata, 2nd edition p.166 Steichen (1998) Begg (t i, v i ), i = 1..., k k t i t = t i = (t i t) (v i )1/2 k j=1 t jv 1 j k j=1 v 1 j k vi = v i t i t j=1 Begg t i v i 25 Begg Egger (t i, v i ) v 1 j t i = t i /v 1/2 i s 1 s 1 = 1/v 1/2 i w i = 1/v i t = α + βs 1 ˆα Funnel Egger ˆβ Harbord et al.(2009) Z ( ) V Z/ V V φ Z = d 1 dn 1 /n 1 8
9 φ = 0 V = n 0 n 1 dh/n 2 (n 1) Peters φ n dh/n Harbord Peters Egger ( )
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